Is There a Cap on Longevity? A Statistical Review

Abstract

There is sustained and widespread interest in understanding the limit, if there is any, to the human life span. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social security systems. A central question is whether the endpoint of the underlying lifetime distribution is finite. Recent analyses of data on the oldest human lifetimes have led to competing claims about survival and to some controversy, due in part to incorrect statistical analysis. This article discusses the particularities of such data, outlines correct ways of handling them, and presents suitable models and methods for their analysis. We provide a critical assessment of some earlier work and illustrate the ideas through reanalysis of semisupercentenarian lifetime data. Our analysis suggests that remaining life length after age 109 is exponentially distributed and that any upper limit lies well beyond the highest lifetime yet reliably recorded. Lower limits to 95% confidence intervals for the human life span are about 130 years, and point estimates typically indicate no upper limit at all. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A Proposal for Finite But Unbounded Human Lifetimes

“…From being non-significantly different to 0, the authors concluded that κ should be taken as exactly zero, indicating an exponential distribution for the data, and argue from this for an unlimited human lifespan. Later ( 14 ) and ( 15 ) updated ( 13 ) with more data and analyses but ultimately still concluded in favour of an exponential model for lifetimes and an unlimited human lifespan.…”

“…Later ( 14 ) and ( 15 ) updated ( 13 ) with more data and analyses but ultimately still concluded in favour of an exponential model for lifetimes and an unlimited human lifespan.…”

“…However, these analyses obtaining non-significant positive (and in some cases non-significant negative) κ values are in fact consistent with those in ( 5 ) and ( 6 ), where the estimated κ are strongly positive. Only limited data from extreme ages is used in ( 13 ), ( 14 ) and ( 15 ), whereas in ( 5 ) and ( 6 ) more extensive data sets spanning ages from 65 on was used, thus obtaining greater statistical power in a demographically-informed model.…”

Introduction: Trends, Puzzles, and Hopes for the Future of Healthcare

“…The topic of aging and longevity is itself a very active area. Researchers are learning about the biology of lifespan by studying bats, whales, naked mole rats, elephants, and albatrosses, among other species (Austad & Finch, 2022;Belzile et al, 2022;da Silva et al, 2022;Eisenstein, 2022;Holmes, 2021;Kaya et al, 2021;Kolora et al, 2021;Lu et al, 2021a;Reinke et al, 2022). A Seychelles giant tortoise (called "Jonathan," hatched c. 1832) is currently the oldest known living land animal.…”

Using a Penalized Likelihood to Detect Mortality Deceleration

“…The theory of unobserved heterogeneity and the associated frailty model (Vaupel et al, 1979) predicts a downward deviation at the oldest ages, to which only the most robust individuals in the population survive. Detecting such a deceleration in real data is not always successful (Gavrilova and Gavrilov, 2015;Newman, 2018), even though the vast majority of studies indicate that death rates at older ages increase at lower rates and can even level off (Curtsinger et al, 1992;Fukui et al, 1993Fukui et al, , 1996Carey et al, 1995;Khazaeli et al, 1998;Gampe, 2010Gampe, , 2021Rootzén and Zholud, 2017;Alvarez et al, 2021;Camarda, 2022;Belzile et al, 2022). In a frailty model setting, testing for mortality deceleration is equivalent to testing whether the non-negative frailty parameter is strictly positive.…”